Mathematics
Differential Equations, 3rd Edition
includes CD-ROM
ISBN-10: 0495012653 ISBN-13: 9780495012658
848 Pages Casebound
© 2006 Published
- Overview
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- About the Author
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- Table of Contents
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- Features
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- New to this Edition
Table of Contents
1. FIRST-ORDER DIFFERENTIAL EQUATIONS.
Modeling via Differential Equations. Analytic Technique: Separation of Variables. Qualitative Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear Equations. Integration Factors for Linear Equations. Review Exercises for Chapter 1. Labs for Chapter 1.
2. FIRST-ORDER SYSTEMS.
Modeling via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. The Lorenz Equations. Review Exercises for Chapter 2. Labs for Chapter 2.
3. LINEAR SYSTEMS.
Properties of Linear Systems and the Linearity Principle. Straight-Line Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex Eigenvalues. Special Cases: Repeated and Zero Eigenvalues. Second-Order Linear Equations. The Trace-Determinant Plane. Linear Systems in Three Dimensions. Review Exercises for Chapter 3. Labs for Chapter 3.
4. FORCING AND RESONANCE.
Forced Harmonic Oscillators. Sinusoidal Forcing. Undamped Forcing and Resonance. Amplitude and Phase of the Steady State. The Tacoma Narrows Bridge. Review Exercises for Chapter 4. Labs for Chapter 4.
5. NONLINEAR SYSTEMS.
Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Periodic Forcing of Nonlinear Systems and Chaos. Review Exercises for Chapter 5. Labs for Chapter 5.
6. LAPLACE TRANSFORMS.
Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Review Exercises for Chapter 6. Labs for Chapter 6.
7. NUMERICAL METHODS.
Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. Review Exercises for Chapter 7. Labs for Chapter 7.
8. DISCRETE DYNAMICAL SYSTEMS.
The Discrete Logistic Equation. Fixed Points and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. Review Exercises for Chapter 8. Labs for Chapter 8.
Hints and Answers.
APPENDICES.
Changing Variables. The Ultimate Guess. Complex Numbers and Euler's Formula.